Find all solutions of the equation in the interval [0,2π) sec(theta) +2=0

I will first reveal the most obvious secret of trig: Most of the problems are 30/60/90 or 45/45/90 triangles of some sort.







The rule to remember is  has solutions

 integer 

Continuing where we left off, a cosine of -1/2 is a 30/60/90 triangle in the second or third quadrant; we pick second, and a little thought tells us the angle is  .





integer 

In the range we want, that's with the plus sign and with the minus, so 

or

or